package algocasts;

public class P76_UniquePaths {
    public int uniquePaths_DP(int m, int n) {
        if (m < 1 || n < 1) return 0;
        int[][] dp = new int[m][n];
        for (int i = 0; i < m; i++) dp[i][0] = 1;
        for (int j = 0; j < n; j++) dp[0][j] = 1;
        for (int i = 1; i < m; i++)
            for (int j = 1; j < n; j++)
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
        return dp[m - 1][n - 1];
    }

    public int uniquePaths_Math(int m, int n) {
        if (m < 1 || n < 1) return 0;
        int small = Math.min(m - 1, n - 1);
        int total = m + n - 2;
        long result = 1;
        for (int i = 0; i < small; i++)
            result = result * (total - i) / (i + 1);
        return (int) result;
    }
}
